pulses [6,7]. In this regime, the notion of thermodynamic equilibrium throughout the semiconductor, with or without external fields, breaks down. Further, experimental approaches sensitive to spatial averages-the case for I-V measurements [8]-or selectively applicable to surfacessuch as scanning-probe-assisted methods [9,10]-become inadequate, and strategies capable of providing local spacecharge information must instead be sought.

As a first step to implementing these ideas, here we use confocal fluorescence microscopy to visualize the dynamics of space-charge formation in diamond. Specifically, we exploit the nitrogen-vacancy (NV) color center as a local probe to reveal charge carrier dynamics in the presence of externally applied voltages. Combining local optical excitation and fluorescent imaging in areas around the point of illumination, we induce and observe the formation of spatial NV fluorescence patterns, whose shapes-themselves a function of the applied electric potentials-allow us to capture the genesis and spatial distribution of space-charge fields. From our experiments, we conclude these fields can reach values comparable to those applied externally (here exceeding 10 6 V=m). Further, we use time-resolved potentials and optical excitation to show that space-charge fields profoundly depend on the preparation protocol, an observation we subsequently build upon to confine and guide carrier propagation.

Figure 1(a) shows a schematic of our experimental setup [11]: We use a custom-made confocal fluorescence microscope combining green (520 nm) and orange (594 nm) lasers, whose timing we control with the help of on-off logic pulses; to reconstruct a fluorescence image, we scan the orange beam across the sample via a precision galvo system. We use a pair of surface metal electrodes connected to a high-voltage power supply and a homemade, highspeed switch to create variable, time-dependent electric fields in a section of the crystal [Fig. 1(b)]. All our measurements below are carried out at room temperature within the 100 μm gap separating the metal pads; we focus the laser beams 10 μm below the diamond surface, with an axial (i.e., depth) resolution of ∼3 μm. Throughout the present experiments, we investigate a type 1b synthetic diamond (DDK) grown via chemical vapor deposition; the nitrogen concentration is 0.25 ppm [12], mostly in the form of neutral substitutional defects or "P1 centers."

In the absence of additional sample treatment, only a small fraction of substitutional nitrogen-about one in a hundred [13]-combine with intrinsic vacancies during crystal growth to form NV centers. Unlike P1 centerswhich are optically dark-NVs have a bright fluorescence spectrum spanning the near infrared [14]. In the presence of green illumination, two-step one-photon processes interconvert NVs between their neutral and negatively charged states [15], producing in the process equal amounts of carriers of either sign, i.e., ionization of an individual NV -leads to injection of one electron, whereas NV 0 recombination produces a free hole. Therefore, even if their concentration is comparatively low, NVs can act as optically activated charge pumps able to provide an endless stream of carriers from a predefined (though arbitrary) location in the crystal. Furthermore, because the fluorescence spectra from neutral and negatively charged NVs overlap only partially, we can make the readout of our microscope selective to only one charge state, which, as we show below, makes it possible to monitor the drift of photogenerated carriers in the applied electric field prior to recapture in a trap.

Figure 1(c) describes our measurement protocol: To charge initialize the NVs, we first scan the green laser throughout the area between the two electrodes. Because the rate of NV -photoionization is lower than the rate of NV 0 recombination, green illumination leaves the NV ensemble preferentially in the negatively charged state [15] (∼75%). We subsequently park the green beam at the midpoint in the interelectrode gap and simultaneously apply a variable voltage to the metal pads. To image the ensuing NV -spatial pattern, we scan the orange laser beam across the area of interest. Although orange excitation can lead to NV -ionization, this process is inefficient at 594 nm [15], implying that a proper selection of the scan parameters (e.g., laser intensity, scanning speed) brings the impact of the readout laser on the NV ensemble to a minimum.

Figure 1(d) summarizes a series of measurements under variable voltages for a green laser park time of 60 s. Rather than the absolute photon counts, images display the differential fluorescence δF obtained upon subtraction of the equivalent fluorescence image in the absence of a green laser park. This procedure allows us to eliminate distortions introduced by uneven excitation and photon collection efficiencies throughout the large field of view required herein (spanning the full interelectrode gap).

In the absence of externally applied fields, carriers of both signs diffuse radially away from the area under illumination toward the bulk of the crystal where they can be recaptured, both by NVs and other defects. Nitrogen-vacancy centers surrounding the point of green excitation transform efficiently into neutral via trapping of diffusing holes, a process likely amplified by Coulombic attraction [16] toward NV -. By contrast, NV 0 recombination via electron capture is negligible [11], thus leading to the formation of a dark, NV 0 -rich "halo" concentric with the point of green excitation [case (i) in Fig. 1(d)]. As the applied voltage increases, we witness a gradual distortion of the cylindrical symmetry and the formation of a dark "tail" indicative of hole drift toward the ground electrode.

To gain an understanding of the system dynamics, we first resort to a set of master equations that take into account carrier photogeneration and trapping as well as diffusive transport and electric-field-driven drift, using ionization and capture parameters derived previously [11]. Assuming NV charge initialization via green excitation, Fig. 2(a) shows the calculated NV charge patterns after a 100-ms-long green park for varying external fields E ext . Comparison with the results in Fig. 1(d) shows the model quickly departs from our observations as it predicts the formation of distinct jetlike patterns, even at fields lower than those applied in our experiments (of order 1 V=μm). This trend changes, however, when the time-varying spacecharge field created by previously trapped carriers-below referred to as the "local" contribution to the space-charge field E sc -is taken into account throughout the laser park time [right lower image in Fig. 2(a); see also Supplemental Material [17] ].

Although the agreement with our observations in Fig. 1 must be deemed qualitative, our modeling shows that the impact of space-charge fields on the system dynamics is amplified in the presence of externally applied potentials. Intuitively, the latter can be understood as a consequence of the charge separation taking place at early stages [Fig. 2(b)], gradually preventing carrier drift toward the electrodes and thus producing the broad, diffusivelike pattern observed experimentally. Unfortunately, using modeling alone to quantify the space-charge field in a class 1b diamond is difficult, as the type and concentration of all defects at play (including their ionization rates and trapping cross sections) is not fully known [12]. Note, however, that nitrogen impurities-presumably assuming positive, neutral, and negative charge configurations via hole and (multi)electron capture [17][18][19][20][21][22]-largely outnumber NVs, implying the latter serve mainly as probes to expose the underlying dynamics.

To more directly gauge the influence of the space-charge field, we implement the experiment in Fig. 3(a). Similar to the protocol in Fig. 1(c), we charge initialize (readout) NV - via a green (orange) laser scan preceding (following) a green laser park. In this case, however, we fraction the park time into a train of n pairs of pulses, each lasting a time t Pj , j ¼ 1, 2, without altering the total park time tP ¼ nðt P1 þ t P2 Þ, which is kept identical to that in Fig. 1. Further, we use a high-speed switch to turn on (off) the electric field during t P1 (t P2 ) throughout the pulse train.

Figure 3(a) shows a collection of NV -differential fluorescence images at increasing voltages. As expected, the charge pattern at zero applied voltage remains unchanged relative to the uninterrupted park [panel (i) in Fig. 1(d)] since the charge dynamics virtually freezes during the dark intervals between laser pulses [6]. As the applied voltage increases, however, the pattern evolves toward a doubly pronged, jetlike shape, dramatically different from that observed in Fig. 1 at comparable voltages. This response can be understood via the conceptual framework of Fig. 2(b); namely, the spacecharge field emerging after t P1 causes carriers created during t P2 to propagate in a direction opposite to that previously induced by E ext , in the process neutralizing E sc at the end of the nth cycle. Correspondingly, carriers produced during t P1 in the ðn þ 1Þth cycle can propagate farther in the direction of E ext , hence resulting in elongated charge patterns, each resembling those calculated in Fig. 2(a). The pattern geometry is indicative of spacecharge fields comparable to those produced externally. Interestingly, we find that optimally short, voltage-free laser pulses (i.e., 0 < t P2 ≪ t P1 ) are sufficient to allow the formation of narrow, one-directional propagation channels [Fig. 3(b)], suggesting that sources other than the local space-charge field-arguably neutralized during t P2 -must also be at play in the observations of Fig. 3(a). We return to this point later.

Much of the discussion above rests on the implicit idea that local space-charge fields combined with trap passivation can steer free carriers in particular directions, a notion we demonstrate with the experiments in Fig. 4(a). This time we create a jetlike charge pattern F 1 using green laser pulses with alternating voltage [protocol in Fig. 3(a)] and subsequently apply an uninterrupted, voltage-free green laser park to create a pattern F 2 . We can then expose the impact of the preexisting charge distribution on carrier propagation through the differential NV -fluorescence image δF 0 ¼ F 2 -F 1 . Figure 4(b) shows the result: The dark contour on the left of the image unmistakably points to carriers propagating along the charge blueprint previously produced during the laser pulse train. Further, the fact that the contour appears exclusively on one side of the pattern indicates that a residual, long-lasting space-charge field accelerates holes to the left. Remarkably, we also find a relative growth of NV -fluorescence within the preexisting blueprint. Unlike the dark contour, the bright pattern features two halves of comparable shape and (differential) intensity, suggesting the underlying mechanism is insensitive to the residual space-charge field. This observation could indicate the formation of excitons-whose binding energy in diamond reaches 70-80 meV [23]-though additional work will be needed to clarify the dynamics of this process.

In addition to this local contribution to the space-charge field, we find that other extended sources play an equally important role. This is shown in Fig. 4(c) where we park the green laser at two locations, (i) and (ii) for long, uninterrupted intervals (protocol in Fig. 1), differing only in the external electric field, active during the first park but not the second. Remarkably, pattern (ii) elongates in a direction opposite to pattern (i), thus revealing a nonlocal field stretching throughout the gap between the electrodes, possibly stemming from carrier traps at the metal-dielectric interface. The amplitude of the tail in pattern (ii) suggests this source of space charge is significant. Future workfor example, using the spin of near-electrode NVs as electric-field sensors [24]-could prove useful to more quantitatively determine the extent and amplitude of these fields.

In conclusion, transport of photogenerated carriers and charge trapping in adjacent defects leads to the formation of strong, metastable space-charge fields, which, in turn, play a dominant role on subsequent carrier propagation. The use of pulsed protocols articulating external voltages and carrier injection allows us to tailor the interplay between carrier propagation and space-charge field formation so as to change the carrier range and/or direction of propagation. Further, the charge patterns that emerge can serve themselves as blueprints to guide carriers along trajectories where trapping is strongly suppressed.

Several intriguing questions are in need of further exploration. For example, throughout our measurements we find that local green excitation leads to an overall reduction of NV -population far away from the point of illumination (note the slightly negative value in the background differential fluorescence of Figs. 1 and3). While we presently cannot rule out the influence of scattered laser light, preliminary observations suggest this effect may instead derive from a form of electric-field insensitive transport, possibly via excitons or exciton complexes [25,26] formed by electron-hole binding during the laser park. Whether or not this type of process is also responsible for the "blurring" of pattern (i) in Fig. 4(c) (observed systematically across multiple analogous experiments) is a closely related question. Further examination is thus warranted, especially given the long range of this effect-exceeding several tens of microns-suggestive of trapping-protected propagation.

As a route to probing space charge in insulators, our strategy is complementary to scanning-probe methods [9,10], higher in resolution but restricted to examining surfaces. It also provides an alternative to acousticor thermal-stimuli methods [27][28][29][30] in that it is lightdiffraction-limited and more naturally adapted to the investigation of small defect ensembles. While the present studies focused on diamond, we anticipate comparable behavior in other wide band gap materials of technological importance. One concrete example is SiC, where charge control of SiV and double-vacancy centers has already been demonstrated and shown to produce long-lived states [31][32][33]. Another illustration is the family of rareearth-doped inorganic insulators-of interest for optical information storage [34] due their long-lasting photochromism [35]-and lanthanide-hosting nitrides such as GaN [36]. Similar ideas could be applicable to mid-and low-band-gap semiconductors in situations where thermal activation is insufficient to establish equilibrium (e.g., systems under cryogenic conditions). Besides the fundamental aspects, our findings may prove relevant to the operation of various semiconducting devices, especially those combining regions of high and low doping (i.e., PIN junctions). Combined with photocurrent measurements, the present techniques could also find use in the investigation of solar cell operation [37,38], in studies to probe the dynamics of magnetoresistance with submicron resolution [39,40], or in the realization of novel quantum technology concepts combining charge and spin [41,42].